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Effects of distributed pressure gradients on the pressure–strain correlations in a supersonic nozzle and diffuser

  • Somnath Ghosh (a1) and Rainer Friedrich (a1)
Abstract

Direct numerical simulation (DNS), based on high-order numerical schemes, is used to study the effects of distributed pressure gradients on the redistribution of fluctuating kinetic energy in supersonic nozzle and diffuser flow with incoming fully developed turbulent pipe flow. Axisymmetric geometries and flow parameters have been selected such that shock waves are avoided and streamline curvature remains unimportant. Although mean extra rates of strain are quite small, strong changes in Reynolds stresses and their production/redistribution mechanisms are observed, in agreement with findings of Bradshaw (J. Fluid Mech., vol. 63, 1974, pp. 449–464). The central role of pressure–strain correlations in changing the Reynolds stress anisotropy is highlighted. A Green’s function-based analysis of pressure–strain correlations is presented, showing remarkable agreement with DNS data.

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Corresponding author
Email address for correspondence: r.friedrich@lrz.tum.de
References
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Adams, N. A. & Shariff, K. 1996 A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems. J. Comput. Phys. 127, 2751.
Bradshaw, P. 1967 The response of a constant-pressure turbulent boundary layer to the sudden application of an adverse pressure gradient. In ARC R and M 3575 Aero. Res. Counc. England.
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. (AGARDograph) , vol. 169. NATO Science and Technology Organization.
Bradshaw, P. 1974 The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers. J. Fluid Mech. 63, 449464.
Coleman, G. N., Fedorov, D., Spalart, P. R. & Kim, J. 2009 A numerical study of laterally strained wall-bounded turbulence. J. Fluid Mech. 639, 443478.
Coleman, G. N., Kim, J. & Spalart, P. R. 2003 Direct numerical simulation of a decelerated wall-bounded turbulent shear flow. J. Fluid Mech. 495, 118.
Duffy, D. G. 2001 Green’s Functions with Applications. Chapman and Hall.
Dussauge, J. P. & Gaviglio, J. 1987 The rapid expansion of a supersonic turbulent flow: role of bulk dilatation. J. Fluid Mech. 174, 81112.
Fernando, E. M. & Smits, A. J. 1990 A supersonic turbulent boundary layer in an adverse pressure gradient. J. Fluid Mech. 211, 285307.
Fernholz, H. H. & Finley, P. J. 1980 A critical commentary on mean flow data for two-dimensional compressible turbulent boundary layers. (AGARDograph) , vol. 253. AGARD.
Fernholz, H. H. & Finley, P. J. 1981 A further compilation of compressible boundary layer data with a survey on turbulence data. (AGARDograph) , vol. 263. AGARD.
Fernholz, H. H., Smits, A. J., Dussauge, J. P. & Finley, P. J. 1989 A survey of measurements and measuring techniques in rapidly distorted compressible turbulent boundary layers. (AGARDograph) , vol. 315. AGARD.
Foysi, H., Sarkar, S. & Friedrich, R. 2004 Compressibility effects and turbulence scalings in supersonic channel flow. J. Fluid Mech. 509, 207216.
Gatski, T. B. & Bonnet, J. P. 2009 Compressibility, Turbulence and High Speed Flow. Elsevier.
Ghosh, S., Foysi, H. & Friedrich, R. 2010 Compressible turbulent channel and pipe flow: similarities and differences. J. Fluid Mech. 648, 155181.
Ghosh, S. & Friedrich, R. 2010 Direct numerical simulation of turbulent flow in an axisymmetric supersonic diffuser. J. Turbul. 11, 122.
Ghosh, S., Sesterhenn, J. & Friedrich, R. 2008 Large-eddy simulation of supersonic turbulent flow in axisymmetric nozzles and diffusers. Intl J. Heat Fluid Flow 29, 579590.
Jayaram, M., Donovan, J. F., Dussauge, J.-P. & Smits, A. J. 1989 Analysis of a rapidly distorted, supersonic turbulent boundary layer. Phys. Fluids 1, 18551864.
Jayaram, M., Taylor, M. W. & Smits, A. J. 1987 The response of a compressible turbulent boundary layer to short regions of concave surface curvature. J. Fluid Mech. 175, 343362.
Lee, J. & Sung, H. J. 2008 Effects of an adverse pressure gradient on a turbulent boundary layer. Intl J. Heat Fluid Flow 29, 568578.
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 1642.
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157, 787795.
Nagano, Y., Tagawa, M. & Tsuji, M. 1993 Effects of adverse pressure gradients on mean flows and turbulence statistics in a boundary layer. In Turbulent Shear Flows (ed. Durst, F., Friedrich, R., Launder, B. E., Schmidt, F. W., Schumann, U. & Whitelaw, J. W.), vol. 8, Springer.
Panchapakesan, N. R., Nickels, T. B., Joubert, P. N. & Smits, A. J. 1997 Lateral straining of turbulent boundary layers. Part 2. Streamline convergence. J. Fluid Mech. 349, 130.
Piomelli, U., Balaras, E. & Pascarelli, A. 2000 Turbulent structures in accelerating boundary layers. J. Turbul. 1, 116.
Poinsot, T. J. & Lele, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104129.
Pompeo, L., Bettelini, M. S. & Thomann, H. 1993 Laterally strained turbulent boundary layers near a plane of symmetry. J. Fluid Mech. 257, 507532.
Saddoughi, S. G. & Joubert, P. N. 1991 Lateral straining of turbulent boundary layers. Part 1. Streamline divergence. J. Fluid Mech. 229, 173204.
Sarkar, S. 1992 The pressure-dilatation correlation in compressible flows. Phys. Fluids A4 (12), 26742682.
Sesterhenn, J. 2001 A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes. Comput. Fluids 30, 3767.
Smith, D. R. & Smits, A. J. 1991 The rapid expansion of a turbulent boundary layer in a supersonic flow. Theor. Comput. Fluid Dyn. 2, 319328.
Smits, A. J. & Dussauge, J. P. 2006 Turbulent Shear Layers in Supersonic Flow. 2nd edn. Springer.
Smits, A. J. & Wood, D. H. 1985 The response of turbulent boundary layers to sudden perturbations. Annu. Rev. Fluid Mech. 17, 321358.
Spalart, P. R. 1986 Numerical study of sink flow boundary layers. J. Fluid Mech. 172, 307328.
Spina, E. F., Smits, A. J. & Robinson, S. K. 1994 The physics of supersonic turbulent boundary layers. Annu. Rev. Fluid Mech. 26, 287319.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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